Nuprl Lemma : assert_of_dset_eq
∀[s:DSet]. ∀[a,b:|s|]. uiff(↑(a (=b) b);a = b ∈ |s|)
Proof
Definitions occuring in Statement :
dset: DSet,
set_eq: =b,
set_car: |p|,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
infix_ap: x f y,
dset: DSet,
implies: P ⇒ Q,
eqfun_p: IsEqFun(T;eq)
Lemmas referenced :
assert_wf,
set_eq_wf,
assert_witness,
equal_wf,
set_car_wf,
dset_wf,
dset_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
isect_memberEquality,
isectElimination,
hypothesisEquality,
axiomEquality,
hypothesis,
lemma_by_obid,
applyEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
because_Cache
Latex:
\mforall{}[s:DSet]. \mforall{}[a,b:|s|]. uiff(\muparrow{}(a (=\msubb{}) b);a = b)
Date html generated:
2016_05_15-PM-00_04_01
Last ObjectModification:
2015_12_26-PM-11_28_54
Theory : sets_1
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